Section:
New Results
Towards a Stochastic Linear Logic for
Biological Computation
Participants :
Kaustuv Chaudhuri, Joëlle Despeyroux.
In previous work [35] ,
Joëlle Despeyroux and Kaustuv Chaudhuri have given an encoding of
the synchronous stochastic -calculus in a hybrid extension of
intuitionistic linear logic (called HyLL). Precisely, they have shown
that focused partial sequent derivations in the encoding are in
bijection with stochastic traces. The modal worlds are used to
represent the rates of stochastic interactions, and the connectives of
hybrid logic are used to represent the constraints in the stochastic
transition rules.
One of the most successful applications of the stochastic
-calculus has been in representing signal transduction networks
in cellular biology. An interesting application of this work would
therefore be the direct representations of biological processes in
HyLL, the original motivation for this line of investigation.
This year, we have worked on specifying some simple examples of regulatory
gene networks, together with basic properties of them—such as stability or
oscillation—in HyLL.
This is ongoing work in collaboration with Gilles Bernot's team at
Nice-Sophia university.
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